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Thursday, October 28, 2010

One thing that struck me about the math talks given at this weekend's New England Conference on the Gifted and Talented was the emphasis on manipulatives and the concerns about whether children understand place value. Are these the most appropriate things to be focusing on when it comes to students who are gifted in math? The mathematically gifted kids I know grasp place value and other aspects of arithmetic with only minimal exposure to manipulatives, and quickly advance to higher levels of abstraction by the time they hit first or second grade. But the education establishment seems bent on convincing itself that children--however gifted--don't understand place value.

Why would you want to convince yourself of this? Because it gives you an excuse not to teach the standard algorithms of arithmetic. If children don't understand place value, then they can't understand borrowing and carrying (regrouping), let alone column multiplication and long division. And unless they understand how these procedures work from the get-go, educators claim (though mathematicians disagree), using them will permanently harm their mathematical development.

So, given how nice it would be not to feel any pressure to teach the standard algorithms (because, let's admit it, they are rather a pain to teach), wouldn't it nice to convince ourselves that our elementary school students, however gifted in math, don't understand place value?

But how do you convince yourself of this? As that ground-breaking math education theorist Constance Kamii has shown, it's child's play. All you have to do is ask a child the right sort of ill-formed question. Here's how it works:

1. Show the child a number like this:

27

2. Place your finger on the left-most digit and ask the child what number it is.

3. When the child answers "two" rather than "twenty," immediately conclude that he or she doesn't understand place value.

4. Banish from your mind any suspicion that a child who can read "27" as "twenty-seven" might simultaneously (a) know that the "2" in "27" is what contributes to twenty-seven the value of twenty and (b) be assuming that you were asking about "2" as a number rather than about "2" as a digit.

Town, county and state governments no longer have much independent political identity. They are mere “conduits for federal mandates,” as Codevilla puts it. He notes that the 132 million Americans who inhabited the country in 1940 could vote on 117,000 school boards, while today a nation of 310 million votes in only 15,000 school districts.

A couple of years ago, when busing costs were at issue here in Irvington, we learned that at some point in NY history the state 'incentivized' (hate that word) districts to consolidate by picking up some of the transportation costs. I no longer recall the details, and the story doesn't make sense given the fact that the town is paying transportation costs, not the state.

But I'm pretty sure the state-incentivizing part is correct in some way, and it's interesting in light of Codevilla's statistics.